Statistical Inference Of Functional Partial Linear Single Index Spatial Autoregressive Model

Spatial econometrics especially the spatial autoregressive(SAR)model is a chief topic.However,a number of researches in SAR field consider cross-section data or panel data.Models based on these two kinds of data rely too much on the linear structure and assumptions,and can’t entirely dispose of the spatial correlation even it sets as a nonlinear form.Economic activities tremendously exist as functional data,containing more information than the data mentioned above.Therefore,how to integrate functional data into the spatial econometric model has become emphasized.Taking the dependence of functional data of spatial economics into account,we extend the functional linear regression in space and construct a series of functional SAR models.Therefore,this dissertation introduces the functional data as an explanatory variable into the single index SAR model,establishing the functional partial linear single index SAR(FPLSISAR)model firstly,which can not only effectively deal with the nonlinear relationship but also avoid dimensional disaster.The results are obtained by quasi maximum likelihood estimation(QMLE),weighted least square method and local linear estimator,and then construct a four-stage estimation method.Subsequently,the Canadian meteorological data are analyzed empirically,finding that the annual total rainfall has negative spatial autocorrelation and positively correlated with the daily average temperature.Secondly,considering the possible individual differences in spatial dependence and the dynamic characteristics of the data,a functional partially linear varying coefficient single index SAR(FPLVCSISAR)model is constructed.The non-parametric generalized method of moment(NPGMM)is harnessed twice to obtain the estimation results taking the heteroscedasticity of the error term into consideration.Then meteorological data of 12 meteorological monitoring stations in Beijing are fitted.Finally,the functional partially linear single-index SAR with SAR disturbances(FPLSISARAR)model is studied.Using the best GMM(BGMM)into the selected best tool variables to build an optimal linear moment condition,obtaining the four-step estimation results of the model.The following is the chapter structure of this dissertation:Chapter 1 introduces the background,significance.By reviewing the relevant literature,introducing the research status of functional regression analysis,SAR model and functional single index model with single index SAR model.Also giving the main research content and the chapter arrangement of the research report,and summarizing the key points,difficulties and innovations.Chapter 2 proposes the FPLSISAR model to explain the influence of functional variables on explained variables in the form of a single index.Firstly,using the local linear estimator to expand the single index link function,then a four-stage estimation basing on QMLE method to estimate the transformed model parameters is constructed.Using the weighted least square method to estimate the functional parameters.The large sample property and theorem-proof of the model are given,and the Monte Carlo simulation is carried out to verify the feasibility of the theory.Subsequently,fitting an empirical analysis of Canadian meteorological spatial data.Chapter 3 extends the FPLSISAR model to the variable coefficient field,and builts the FPLVCSISAR model.Combined with local linear expansion and least square estimation,this dissertation establishes a three-stage estimation method based on the NPGMM method.By using Taylor expansion and standard orthogonal trigonometric function system,the variable coefficient and single index are partially expanded.The parameter estimation results are obtained through twice NPGMM with the local and global instrumental variables.Then,the large sample property and theorem-proof of the model are given,and the estimation method design algorithm of the model is simulated randomly.Finally,the empirical analysis of Beijing meteorological data is carried out.Chapter 4 extends the error term of FPLSISAR model to the space domain and constructs the FPLSISARAR model.Combining local linear expansion and least squares estimation,a four-stage estimation method based on the BMM method is established.Achieving the preliminary estimates of the model by two stage least square(2SLS)and QMLE,the best instrumental variable matrix is constructed,and are updated parameters by minimizing the sum of squares of residuals.Then,the large sample property and theorem-proof of the FPLSISARAR model are given,and the estimation method of the model is simulated finally.Chapter 5 sums up the main points and insufficient,then begins to look ahead the content that can be further studied.